• question_answer Case Study : Q. 21 to 25 The resident welfare association of a Radheshyam society decided to build two straight paths in their neighbourhood park such that they do not cross each other and also plan trees along the boundary lines of each path. One of the members of association Shyam Lal suggested that the paths should be constructed represented by the two linear equations $\text{x}-\text{3y}=\text{2}$and$-\text{2x+6y}=\text{5}$. Based on the above information, give the answer of the following questions. If the pair of equations ${{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0$ and ${{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0$ has infinitely solutions, then condition is: A) $\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}$ B) $\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}$ C) $\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}$ D) $None\,\, of\,\, these$

 If the pair of equation ${{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0$ and ${{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0$ has infinitely solutions, then condition is $\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}$ So, option [b] is correct.